Fractals in Real Life

Date: 10/04/1999 at 09:09:21
From: Kristin Argotsinger
Subject: The use of fractals in real world life.
How are fractals used by scientists and mathemeticians in the real
world today?
I know what a fractal is and have a good amount of background
information on them, but I can not think of how they are used in the
real world today.
Thank you for your time!
Kristin Argotsinger

Date: 10/05/1999 at 21:48:28
From: Doctor Douglas
Subject: Re: The use of fractals in real world life.
Hi Kristin,
This is a great question! As you know, fractals describe geometrical
objects that have more and more sub-structure as one views them at
higher and higher magnifications. An excerpt from the sci.nonlinear
FAQ at
http://amath.colorado.edu/appm/faculty/jdm/faq.html
says that
"Fractals also approximately describe many real-world objects, such
as clouds, mountains, turbulence, coastlines, roots and branches of
trees and veins and lungs of animals."
Scientists and engineers and mathematicians and other people
interested in these objects (such as a computer graphics person
working to create an image of an artificial landscape) might use
fractals in their work. For example, a biomedical engineer might want
to calculate how much surface area covers the bronchial tubes within a
human lung. Or maybe an environmentalist wants to estimate how many
miles of coastline could be affected by a large oil spill. These are
ways that scientists use fractals to describe or approximate the
*structure* of a real (or imagined) object.
Another way scientists and mathematicians sometimes use fractals
is in the field of nonlinear dynamics, where the behavior of a system
is *described* by a geometrical object in something called "phase
space." This object can assume many different forms, such as points
or loops (circles, polygons, squashed ellipses, etc.). Points indicate
the situation when there is no change in behavior, while loops
describe when a system does the same thing over and over again
continuously, (i.e. it "oscillates"). An example of another shape is a
spiral. Dynamicists use the spiral to describe how a pendulum swings
back and forth and gradually spirals into the origin as time goes on.
As for fractals, there are some behaviors (often called "chaotic")
that are so complex that the geometric object is a fractal, rather
than a simpler shape. A cardiologist might monitor a patient's
heartbeat and chart its behavior over time. A healthy patient might
have a slightly irregular heartbeat, and this might be visible in the
record as a fractal. But if the heartbeat becomes too regular, the
fractal might morph into a simpler shape, such as a loop, indicating
that the patient might be at risk for a heart attack. In this example
the fractal is used to help the physician monitor the status of her
patient.
So you see that fractals can be used to describe the *structure* of
things in the real world, or the *behavior* of systems in time.
Hope this helps. If anything in this response is confusing to you,
please don't hesitate to write back. For more information, you might
wish to visit the nonlinear FAQ (URL above) or the fractal FAQ at
ftp://rtfm.mit.edu/pub/usenet/news.answers/fractal-faq
Good luck!
- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/